Question: Simplify the following expression: $z = \dfrac{t^2 + 6t - 27}{t - 3} $
Explanation: First factor the polynomial in the numerator. $ t^2 + 6t - 27 = (t - 3)(t + 9) $ So we can rewrite the expression as: $z = \dfrac{(t - 3)(t + 9)}{t - 3} $ We can divide the numerator and denominator by $(t - 3)$ on condition that $t \neq 3$ Therefore $z = t + 9; t \neq 3$